Mechanical Properties of Solids | Class 11 Physics Notes

8.2 Stress and strain

This section defines stress and strain, fundamental quantities to describe deformation in solids under applied forces. When a body is subjected to forces but remains in static equilibrium, it may deform slightly or largely depending on the material and force magnitude. The deformation produces internal restoring forces equal and opposite to the applied forces. Stress is defined as the restoring force per unit area acting inside the body. If a force F acts normal to a cross-sectional area A, the magnitude of stress is F/A. The SI unit of stress is Newton per square meter (N/m²) or Pascal (Pa). Stress can be tensile (stretching), compressive (squeezing), or shearing (forces applied tangentially). Corresponding to these stresses, strains are defined as fractional changes in length or shape. Longitudinal strain is the fractional change in length ΔL/L under tensile or compressive stress. Shearing strain is the ratio of relative displacement Δx between opposite faces to the length L, approximately equal to the small angular displacement θ in radians. Volume strain occurs under hydraulic stress (pressure applied uniformly), defined as fractional change in volume ΔV/V. Strain is dimensionless as it is a ratio of lengths or volumes. The section also describes different types of stresses with diagrams: tensile/compressive stress elongates or compresses a cylinder; shearing stress causes angular deformation; hydraulic stress compresses a body uniformly without changing shape.

📊 Diagram: Fig. 8.1 (a) A cylindrical body under tensile stress elongates by ΔL (b) Shearing stress on a cylinder deforming it by an angle θ (c) A body subjected to shearing stress (d) A solid body under a stress normal to the surface at every point (hydraulic stress). The volumetric strain is ΔV / V, but there is no change in shape.

🔗 Connection: Prepares for the next section on Hooke's law, which relates stress and strain linearly for small deformations.